Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball
Date
2008Source
Proceedings of the London Mathematical SocietyVolume
97Issue
2Pages
477-513Google Scholar check
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Weighted Triebel-Lizorkin and Besov spaces on the unit ball Bd in d with weights wμ(x)=(1-x2)μ-1/2, μ≥0, are introduced and explored. A decomposition scheme is developed in terms of almost exponentially localized polynomial elements (needlets) φξ, ψξ and it is shown that the membership of a distribution to the weighted Triebel-Lizorkin or Besov spaces can be determined by the size of the needlet coefficients 〈f, φξ〉 in appropriate sequence spaces. © 2008 London Mathematical Society.